\documentclass{standalone}
\usepackage{TangramTikz}

\begin{document}

% No one can deny that this is a cat.
\begin{EnvTangramTikz}
		\PieceTangram[TangSol]<rotate = 45>({2 - sqrt(2)}, {2 + sqrt(2)}){TangCar}
		
		\PieceTangram[TangSol]<rotate = 0>({0}, {0}){TangGrandTri}
		
		\PieceTangram[TangSol]<rotate = 45>({2 - sqrt(2)},{2 - sqrt(2)}){TangGrandTri}
		
		\PieceTangram[TangSol]({2}, {0}){TangPara}
		
		% This is the left ear
		\PieceTangram[TangSol]<rotate = 45>({2 - 1.5 * sqrt(2)}, {2 + 1.5 * sqrt(2)}){TangPetTri}
		
		% This is the right ear, just rotated by -135 degrees.
		\PieceTangram[TangSol]<xscale = -1, yscale = -1, rotate = -315>({2-0.5 * sqrt(2)}, {2 + 2.5 * sqrt(2)}){TangPetTri}
		
		\PieceTangram[TangSol]<rotate = 90>({2 - sqrt(2)}, {sqrt(2)}){TangMoyTri}
\end{EnvTangramTikz}

\end{document}